Question

The sum of two numbers is 84. If four times the smaller number is subtracted from the larger number the result is 14. Find the two numbers

Answer 1

y=14

Explanation:

x + y = 84

-1(x - 4y = 14)

-x + 4y = -14

x + y = 84

-x + 4y = -14

5y = 70

divide by 5

y = 14

Answer 2

Answer: 70 and 14

Explanation:

Let the bigger number be x and the smaller number be y , then from the first statement

`x + y = 84`

From the second statement :

four times the smaller number means
`4` x
`y` , which will be
`4y` , so

four times the smaller number is subtracted from the larger number the result is 14 means :

`x - 4y = 14`

combining the two equations we have :

`x + y = 84` ........................... equation 1

`x - 4y = 14` .......................... equation 2

solving the system of linear equation by substitution method , from equation 1 , make x the subject of the formula , that is :

`x = 84 - y` .......................... equation 3

substitute
`x = 84 - y` into equation 2 , that is

`84 - y - 4y = 14`

`84 - 5y = 14`

`84 - 14 = 5y`

`70 = 5y`

therefore :

`y = 14`

substitute
`y = 14` into equation 3 to find the value of x

`x = 84 - y`

`x = 84 - 14`

`x = 70`

check :

`x + y = 84`

`70 + 14 = 84`

`x - 4y = 14`

`70 - 4( 14 )`

`70 - 56 = 14`

Therefore : the bigger number is 70 and the smaller number is 14